We have studied the stress-strain hysteresis loops during the martensitic transition of a Cu-Zn-Al single crystal. The transition was mechanically induced either under stress-driven or strain-driven conditions. The comparison between the two mechanisms shows significant differences in the transformation path. In situ optical observations in strain-driven experiments reveal retransformation which results in a re-entrant behaviour. No re-entrancy is found in stress-driven experiments. The hysteresis is larger in stress-driven experiments.